Quantum
Hypothesis
Learning Objectives:
By the end of this chapter, you wil
l be able to:
♦ Define concepts of Blackb
ody Radiation.
♦ Explain basics of Planck
's quantum hypothesis.
♦ Describe concept of Par
ticle Picture of Radiation.
♦ Understand Photoelectr
ic effect.
♦ Learn about X-Ray and
X-Ray concepts.
♦ Interpret Wave-Particl
e Duaility principle.
24 .1 IN TR OD UC TI ON
The aim of physics is to understand
the natural phenomena around us. th
rapid growth in physics. Newtonian 19 century witnessed a
mechanics was nearly perfected and
the fields of electricity and magnetism Maxwell synthesized
into a single theory which permitted
into the frame work of electromagn inclusion of optics
etic phenomenon. Towards the end
was generally believed that all that of the 19 th century it
to be discovered in nature was discov
of nature were fonnulated. The Ne ered, and all the laws
wtonian mechanics, Maxwell's ele
them1odynamics came to be known ctromagnetic theory and
later as classical physics. Classical
_assuming that particles are localized physics was developed
and we can observe them without app
them. The three laws of conservat reciably disturbing
ion, namely conservation of linear
momentum and energy formed the momentum, angular
basis for classical mechanics. Howe
followed dispelled such illusions ver ver, discoveries that
y soon.
At about the turn of 20 th century
a number of fundamental discoveri
which could not be explained within es were reported
the framework of the above classical
The inadequacy of classical theori theories of physics.
es was noticed first when they we
black body radiation emitted by a bod re applied to explain the
y hotter than its surroundings. To exp
radiation, Max Planck put forward lain the blackbody
a revolutionary hypothesis that the
emit energy not continuously but molecules in a source
in small discrete packets called qua
departure from the classical theory nta . This was a radical
and contrary to day-to-day experi
ence. Einstein made
589
- - - - - - --
,590 A Textbook of Engineering Physics
use of Planck's hypothesis that a quantum of radiation carries an energy hv and sue
explained the photoelectric effect. Other experimental results also showed that the ~ ssf~lly
concepts were entirely inadequate and one has to invoke the quantum concept to exp\ a~sica\
behaviour of atoms and subatomic particles. A new body of ideas based on Planck's woaikn th e
developed, and the new theory came to be known as quantum Ph ys1cs. . r was
Quantum ph .
.
explains the behaviour of matter and radiation at the m1crosc . . ,1 l Ysics
op1c I1atomzc 1 eve/.
24.2 WAVE-PICTURE OF RADIATION-EN ERG Y FLOW IS
CONT INUO US
We are familiar with several waves such as radio waves, microwaves, heat waves, light
waves, UV-rays, X-rays and y-rays etc. These waves constitute a single family called electro-
magnetic waves or simply radiation. Electromagnetic waves comprise varying electric
and
magnetic fields traveling in space at the velocity of 'c'. The propagation of electromagnetic
waves and their interaction with matter is explained with the help of Maxwell's electromag-
netic theory.
Maxwell's theory considered the process of emission of radiation by a source as a
continuous process. A heated body may be supposed to be capable of emitting energy that
travels in the form of waves of all possible wavelengths. In the same manner, the radiation
incident on a body may be thought to be absorbed at all possible wavelengths. The intensi~·
of radiation is given by
I= IEl 2 ... (24. l)
where E is the amplitude of the electromagnetic wave.
24.3 BLACKBODY RADIATION
It is well known that when a body is heated, it emits electromagnetic radiation . ~e
radiation emitted by the source by virtue of its temperature is called thermal radiat1on.
Thermal radiation is electromagnetic in nature and its energy is smoothly distributed oYer
all wavelengths. Thus, a thermal source produces continuous spectrum. The mtensi . ·ty and
.
the predominant wa~e~ength _of ra~ia~ion v~ry with the temperature of the bod~-
temperatures the radiation mamly hes m the mfrared region. As the temperature of the -~
At;::
is increased, the component of maximum intensity sh°ifts to a higher and higher frequend\~
For example, the filament of an incandescent bulb appears dark at room tempera~rc an ,~~-
current is passed, it gets heated up. As the current increases through the filament. it ap~$
initially red, orange gradually and yellow and finally it emits white light. At tem~rtl\. all
above l 000°C, a heated body is capable of giving out energy in the fom1 of wav~,~~s (10
possible wavelengths. Normally the amount of radiation emitted by a hot body de~ 11 - . J
factors such as the properti.es of.its surface. Apart from emitting electromagneuc
. .. rad1at 100
·
body also absorbs electromagnetic radiation incident on it. c~biJY
A body that absorbs the entire radiation incident on it is called a perfect ~/~ a ~~iJ:
Wh_en a perfect blackbody is heated, it emits ~d~ation at all frequencies and
radiator as well as a good absorber. The radwt10n emitted by a petfect b/ackb
1
t~u~tt
;., (i ' ;
1
.,
blackbody radiation . , i,,· 1J t~~
ru1 d~
In practice, there_ are no pe~f~ct blackbodies b_ut _an ideal_black body ~an be-~rfacc i,_ · '\J1c'<
~·\-ti t'
a hollow sphere (cavity) and dnllmg a small hole 1111t (sec fi g. 24.1 ). Its rnnt'r:,, , it1 ,cr :,ll
with lampblack. Any radiation entering the cavity through O is incidt.ml on th ' 1 ,
A
, Chapter 2..J Qua ntum Hyp othe sis
_ ,.:a ,·ity and is part ly absorbed and 591
r" _ refl ected. The reflected component
is :r.1..·, dent at another point on the inner
,wt -i i..:c " here again it is partly absorbed
3 nu panly reflected . Thus, light entering
1:--i: 1.·a,·i ty undergoes multiple
Incident
reflections radiation
'. 1! the walls and gets trap
0
ped inside the
_- .i\ ity. The probability of
the radiation
,_ an y wavelength escaping out of the 'Ho le
t·. ,\e is negli_gi ble. Hence, the
hole acts
., perfec t abso rber and appears perfectly
:!ark. Conversel y, when the cavity is
· ,~a1ed, the radiation produced in the
Fig. 24.1:
·: cis i ty comes out through the aper
ture
:rnd contains all the wavelengths. Illustration of blac kbod y
There fore, the hole acts as a perfect
::,i-nitter and has the characteristics of T = 5500K
ti lackbody radiation. Its spectrum can
800
be analyzed by an infrared spectrometer
usin g a bolometer as a detector. Thus,
.he emissive power of the blackbody at ~
600
different wavelengths can be determined. EC T = 5000K
if the distribution of radiant energy as 6 -- 1·'-,
/ ·, \
a !'unction of wavelength at different 2 400 / \
:J /
I '\
'.1.· rn peratures is plotted, we obtain a set of / T = 4500K \
I '
. mv es as show n in Fig. 24.2. i
The experimental results (Fig. 24.2) 200 I
1how that at a given temperature the I
, ,.,di ation energy density initially increases
.,, ith increasing wavelength then peaks 00 500 1000 1500 2000
11 around a particular wavelen
gth Am "A (nm)
ind after that decreases finally to zero Fig. 24.2:
- t very high wavelengths. The
spectral Radiation ener gy dens ity vers us wav elen
gth
<:; istribution of that radiation is a function at a given temp erat ure
,_ if tem perature alone and the materfal as
,uc h plays no role .
.!4 .3 . l Law s of Bla ckb ody Rad iati on
(i) Stefan-Boltzmann law: The Stefan-B
oltzmann law is an empirical relationship obtained
by Stefan and later derived theoretically by
Boltzmann. 1t connects the intensity of
radiation to the temperature. It states that the
total radiation emit ted from a blackbody
at temp erat ure Tis prop orti ona l to the fourth
pow er of the absolute temperature of the
bod y r1.
E=a r4 ... (24. 2)
where cr is called Stefan's constant having a num 4
erical value of 5.67 x 1o-8 WI rn 2-K ·
(ii) Wien's law: It is seen from Fig. 24.2 that the value of
Am depends only on t~e
temperature T of the blackbody and decrease
s with increasin g temp erature. Am 15
Hypothesis
Learning Objectives:
By the end of this chapter, you wil
l be able to:
♦ Define concepts of Blackb
ody Radiation.
♦ Explain basics of Planck
's quantum hypothesis.
♦ Describe concept of Par
ticle Picture of Radiation.
♦ Understand Photoelectr
ic effect.
♦ Learn about X-Ray and
X-Ray concepts.
♦ Interpret Wave-Particl
e Duaility principle.
24 .1 IN TR OD UC TI ON
The aim of physics is to understand
the natural phenomena around us. th
rapid growth in physics. Newtonian 19 century witnessed a
mechanics was nearly perfected and
the fields of electricity and magnetism Maxwell synthesized
into a single theory which permitted
into the frame work of electromagn inclusion of optics
etic phenomenon. Towards the end
was generally believed that all that of the 19 th century it
to be discovered in nature was discov
of nature were fonnulated. The Ne ered, and all the laws
wtonian mechanics, Maxwell's ele
them1odynamics came to be known ctromagnetic theory and
later as classical physics. Classical
_assuming that particles are localized physics was developed
and we can observe them without app
them. The three laws of conservat reciably disturbing
ion, namely conservation of linear
momentum and energy formed the momentum, angular
basis for classical mechanics. Howe
followed dispelled such illusions ver ver, discoveries that
y soon.
At about the turn of 20 th century
a number of fundamental discoveri
which could not be explained within es were reported
the framework of the above classical
The inadequacy of classical theori theories of physics.
es was noticed first when they we
black body radiation emitted by a bod re applied to explain the
y hotter than its surroundings. To exp
radiation, Max Planck put forward lain the blackbody
a revolutionary hypothesis that the
emit energy not continuously but molecules in a source
in small discrete packets called qua
departure from the classical theory nta . This was a radical
and contrary to day-to-day experi
ence. Einstein made
589
- - - - - - --
,590 A Textbook of Engineering Physics
use of Planck's hypothesis that a quantum of radiation carries an energy hv and sue
explained the photoelectric effect. Other experimental results also showed that the ~ ssf~lly
concepts were entirely inadequate and one has to invoke the quantum concept to exp\ a~sica\
behaviour of atoms and subatomic particles. A new body of ideas based on Planck's woaikn th e
developed, and the new theory came to be known as quantum Ph ys1cs. . r was
Quantum ph .
.
explains the behaviour of matter and radiation at the m1crosc . . ,1 l Ysics
op1c I1atomzc 1 eve/.
24.2 WAVE-PICTURE OF RADIATION-EN ERG Y FLOW IS
CONT INUO US
We are familiar with several waves such as radio waves, microwaves, heat waves, light
waves, UV-rays, X-rays and y-rays etc. These waves constitute a single family called electro-
magnetic waves or simply radiation. Electromagnetic waves comprise varying electric
and
magnetic fields traveling in space at the velocity of 'c'. The propagation of electromagnetic
waves and their interaction with matter is explained with the help of Maxwell's electromag-
netic theory.
Maxwell's theory considered the process of emission of radiation by a source as a
continuous process. A heated body may be supposed to be capable of emitting energy that
travels in the form of waves of all possible wavelengths. In the same manner, the radiation
incident on a body may be thought to be absorbed at all possible wavelengths. The intensi~·
of radiation is given by
I= IEl 2 ... (24. l)
where E is the amplitude of the electromagnetic wave.
24.3 BLACKBODY RADIATION
It is well known that when a body is heated, it emits electromagnetic radiation . ~e
radiation emitted by the source by virtue of its temperature is called thermal radiat1on.
Thermal radiation is electromagnetic in nature and its energy is smoothly distributed oYer
all wavelengths. Thus, a thermal source produces continuous spectrum. The mtensi . ·ty and
.
the predominant wa~e~ength _of ra~ia~ion v~ry with the temperature of the bod~-
temperatures the radiation mamly hes m the mfrared region. As the temperature of the -~
At;::
is increased, the component of maximum intensity sh°ifts to a higher and higher frequend\~
For example, the filament of an incandescent bulb appears dark at room tempera~rc an ,~~-
current is passed, it gets heated up. As the current increases through the filament. it ap~$
initially red, orange gradually and yellow and finally it emits white light. At tem~rtl\. all
above l 000°C, a heated body is capable of giving out energy in the fom1 of wav~,~~s (10
possible wavelengths. Normally the amount of radiation emitted by a hot body de~ 11 - . J
factors such as the properti.es of.its surface. Apart from emitting electromagneuc
. .. rad1at 100
·
body also absorbs electromagnetic radiation incident on it. c~biJY
A body that absorbs the entire radiation incident on it is called a perfect ~/~ a ~~iJ:
Wh_en a perfect blackbody is heated, it emits ~d~ation at all frequencies and
radiator as well as a good absorber. The radwt10n emitted by a petfect b/ackb
1
t~u~tt
;., (i ' ;
1
.,
blackbody radiation . , i,,· 1J t~~
ru1 d~
In practice, there_ are no pe~f~ct blackbodies b_ut _an ideal_black body ~an be-~rfacc i,_ · '\J1c'<
~·\-ti t'
a hollow sphere (cavity) and dnllmg a small hole 1111t (sec fi g. 24.1 ). Its rnnt'r:,, , it1 ,cr :,ll
with lampblack. Any radiation entering the cavity through O is incidt.ml on th ' 1 ,
A
, Chapter 2..J Qua ntum Hyp othe sis
_ ,.:a ,·ity and is part ly absorbed and 591
r" _ refl ected. The reflected component
is :r.1..·, dent at another point on the inner
,wt -i i..:c " here again it is partly absorbed
3 nu panly reflected . Thus, light entering
1:--i: 1.·a,·i ty undergoes multiple
Incident
reflections radiation
'. 1! the walls and gets trap
0
ped inside the
_- .i\ ity. The probability of
the radiation
,_ an y wavelength escaping out of the 'Ho le
t·. ,\e is negli_gi ble. Hence, the
hole acts
., perfec t abso rber and appears perfectly
:!ark. Conversel y, when the cavity is
· ,~a1ed, the radiation produced in the
Fig. 24.1:
·: cis i ty comes out through the aper
ture
:rnd contains all the wavelengths. Illustration of blac kbod y
There fore, the hole acts as a perfect
::,i-nitter and has the characteristics of T = 5500K
ti lackbody radiation. Its spectrum can
800
be analyzed by an infrared spectrometer
usin g a bolometer as a detector. Thus,
.he emissive power of the blackbody at ~
600
different wavelengths can be determined. EC T = 5000K
if the distribution of radiant energy as 6 -- 1·'-,
/ ·, \
a !'unction of wavelength at different 2 400 / \
:J /
I '\
'.1.· rn peratures is plotted, we obtain a set of / T = 4500K \
I '
. mv es as show n in Fig. 24.2. i
The experimental results (Fig. 24.2) 200 I
1how that at a given temperature the I
, ,.,di ation energy density initially increases
.,, ith increasing wavelength then peaks 00 500 1000 1500 2000
11 around a particular wavelen
gth Am "A (nm)
ind after that decreases finally to zero Fig. 24.2:
- t very high wavelengths. The
spectral Radiation ener gy dens ity vers us wav elen
gth
<:; istribution of that radiation is a function at a given temp erat ure
,_ if tem perature alone and the materfal as
,uc h plays no role .
.!4 .3 . l Law s of Bla ckb ody Rad iati on
(i) Stefan-Boltzmann law: The Stefan-B
oltzmann law is an empirical relationship obtained
by Stefan and later derived theoretically by
Boltzmann. 1t connects the intensity of
radiation to the temperature. It states that the
total radiation emit ted from a blackbody
at temp erat ure Tis prop orti ona l to the fourth
pow er of the absolute temperature of the
bod y r1.
E=a r4 ... (24. 2)
where cr is called Stefan's constant having a num 4
erical value of 5.67 x 1o-8 WI rn 2-K ·
(ii) Wien's law: It is seen from Fig. 24.2 that the value of
Am depends only on t~e
temperature T of the blackbody and decrease
s with increasin g temp erature. Am 15
